Dissertation/Thesis Abstract

Quasi-Baer and FI-Extending Generalized Matrix Rings
by Davis, Donald D., Ph.D., University of Louisiana at Lafayette, 2018, 56; 10932375
Abstract (Summary)

Generalized Matrix rings are ubiquitous in algebra and have relevant applications to analysis. A ring is quasi-Baer ( right p.q.-Baer) in case the right annihilator of any ideal (resp. principal ideal) is generated by an idempotent. A ring is called biregular if every principal right ideal is generated by a central idempotent. A ring is called right FI-extending ( right strongly FI-extending) if every fully invariant submodule is essential in a direct summand (resp. fully invariant direct summand). In this paper we identify the ideals and principal ideals, the annihilators of ideals and the central, semi-central and general idempotents of a 2 × 2 matrix ring. We characterize the generalized matrix rings that are quasi-Baer, p.q.-Baer and biregular and we present structural features of right FI-extending and right strongly FI-extending rings. We provide examples to illustrate these concepts.

Indexing (document details)
Advisor: Birkenmeier, Gary F.
Commitee: Heatherly, Henry E., Lynd, Justin, Magidin, Arturo
School: University of Louisiana at Lafayette
Department: Sciences
School Location: United States -- Louisiana
Source: DAI-B 80/08(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Biregular, FI-extending, Generalized matrix rings, Idempotents, Quasi-Baer, p.q. Baer
Publication Number: 10932375
ISBN: 978-1-392-04194-9
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